Optimal control of PDEs in a complex space setting: application to the Schrödinger equation. (English) Zbl 1412.49051
Summary: In this paper, we discuss optimality conditions for abstract optimization problems over complex spaces. We then apply these results to optimal control problems with a semigroup structure. As an application we detail the case when the state equation is the Schrödinger one, with pointwise constraints on the “bilinear” control. We derive first and second order optimality conditions and address, in particular, the case that the control enters affine in the cost function.
MSC:
| 49K27 | Optimality conditions for problems in abstract spaces |
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 35J10 | Schrödinger operator, Schrödinger equation |
Keywords:
optimal control; partial differential equations; optimization in complex Banach spaces; second order optimality conditions; Goh transform; semigroup theory; Schrödinger equation; bilinear control systemsReferences:
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